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Exploring the Distributive Property in Addition and Multiplication

In this lesson, we explore the distributive property to solve problems involving multiples and total costs. For example, if you buy 5 CDs for $8 each and 7 more for the same price, you can calculate the total cost by finding the individual products or by using the total number of CDs. The lesson also covers why the sum of two multiples remains a multiple of the same number, demonstrated through algebraic and pictorial methods. Engage with a partner for a deeper understanding and apply the distributive property to various addition scenarios.

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Exploring the Distributive Property in Addition and Multiplication

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  1. Adding Multiples-Using Distributive Property

  2. Explore with a partner for 5-10 minutes Yesterday I bought 5 CDs at the music store. Each one cost $8. Today I bought 7 CDs at $8 each. How can I find the total cost of all CDs? 1. We can show the cost of yesterday's CDs by finding the product of 5 and $8. 2. We can show the cost of today's CDs by finding the product of 7 and $8. + 5 x $8 7 x $8 + $56 $40 $96

  3. Now lets find the cost by first finding the total number of CDs then multiplying by the cost of one CD.

  4. Nina was finding multiples of 6. • She said, 18 and 42 are both multiples of 6, and when I add them, I also get a multiple of 6: 18+42 = 60. • Explain to Nina why adding two multiples of 6 will always result in another multiple of 6.

  5. Solution: Using Pictures **18 and 42 are both multiples of 6 which means 6 is a factor of both numbers. 6⋅3=18 6⋅7=42

  6. When you add 18 and 42, you can use the distributive property to show that the sum is also a multiple of 6: 6⋅3+6⋅7=6⋅(3+7)=6⋅10

  7. Solution: An Algebraic Explanation • If you have any two multiples of 6, you can write them both as 6 times a whole number. We can write this in symbols as 6a 6b (where a and b are both whole numbers). • When you add them, you have 6a + 6b = 6(a + b) • Since a and b are whole numbers, so is a + b. So the sum of two multiples of 6 is always a multiple of 6. **Please note that there is nothing special about 6 in this argument, so it will work exactly the same way with any whole number in place of 6.

  8. Find Sums Using the Distributive Property • 24 + 16 • 36 + 15 • 40 + 25 • 42 + 12 • 48 + 28 • 54 + 36

  9. Use the Distributive Property to find the area of this figure. 9cm 4cm 13cm

  10. Use the distributive property to solve this problem mentally4*56=

  11. You go to the supermarket. 1 bag of apples costs 4 dollars. 1 gallon of olive oil costs 10 dollars. You get 6 bags of apples and 6 gallons of olive oil. How much money do you pay the cashier? • $14 • $12 • $84 • $168 Use Distributive Property

  12. I feel comfortable using the distributive property to find the sum of two numbers. • Strongly Agree • Agree • Disagree • Strongly Disagree

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